visualization of air flow in vortex tube using different

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Visualization of air flow in vortex tube using different turbulence models

IntroductionAt present time most buildings are equipped with

state-of-the-art climate systems allowing maintenance of optimum values of humidity and air temperature with-in all rooms. In a winter season these systems carry out heating air in a building and in summertime provide its cooling. The principle of operation of such systems is generally based on thermodynamic cycles of coolants and such systems used to be called chillers. The typical coolants are Freon and ammonia which are not ecologi-cal ones. Chillers also have other essential disadvantages such as design complexity, high labour-output ratio and presence of toxic substances. Nevertheless chillers are widespread in civil engineering field despite their disad-vantages.

Alternative way of cooling and heating is the use of Ranque-Hilsch vortex tubes [1, 2]. Atmosphere air is usually used in thermodynamic cycle of such devices to produce heat flow. The same air can be also used as a heat carrier. Therefore vortex tubes are often considered

as ecological devices. They have very simple design and structure, low labour-output ratio and some other ben-efits.

In spite of the benefits, vortex tubes have low energy efficiency. The value of isentropic energy efficiency coef-ficient calculated by equation (1) is usually lower than 0.4. This is the reason why vortex tubes cannot be used widely.

hSX

S

I

I=DD (1)

where ΔIx — total enthalpy difference between inlet and cold flows of the vortex tube; ΔIS — total enthalpy difference arising in the ideal isentropic gas expansion from the inlet to outlet pressure.

A schematic of vortex tube is shown in Fig. 1. Compressed gas is injected into the energy separation chamber through the nozzle inlet. As a result, vortex flow appears in that chamber. Outer part of the vortex flow has higher total temperature as compared the core flow. Finally, cold and hot flows are discharged at different sides of the vortex tube [1, 2].

DOI 10.15826/rjcst.2015.1.009 УДК 533

Noskov A. S.1, Alekhin V. N.2, Khait A. V.3, Anoshin N. M.4 1–4 Ural Federal University,Yekaterinburg, Russia

E-mail: 1, [email protected], [email protected], [email protected]

vISUALIZATION OF AIR FLOW IN vORTEx TUBE USING DIFFERENT TURBULENCE MODELS

Abstract. Visualization of air flow in Ranque-Hilsch vortex tube performed by numerical simulations with standard k-ε and SAS-SST turbulence models is presented in the paper. SAS-SST turbulence model predicted the existence of secondary large-scale vortex structures within the computational domain instead k-ε model showed axisymmetrical flow. Existence of large-scale secondary vortex structures is in agreement with experimental data.

Keywords: Ranque-Hilsch effect, vortex tube, CFD, turbulence modeling, visualization.

Носков А. С.1, Алехин В. Н.2, Хаит А. В.3, Аношин Н. М.4 1–4 Уральский федеральный университет,Екатеринбург, Россия

E-mail: 1, [email protected], [email protected], [email protected]

ВИЗУАЛИЗАцИЯ ПОТОКА ВОЗДУХА В ВИХРЕВОЙ ТРУбЕ С ИСПОЛЬЗОВАНИЕМ РАЗЛИчНЫХ МОДЕЛЕЙ ТУРбУЛЕНТНОСТИ

Аннотация. В статье представлены результаты визуализации потока воздуха в вихревой трубе Ранка-Хилша, выпол-ненной с помощью численного моделирования. Были использованы k-ε и SAS-SST модели турбулентности. SAS-SST модель турбулентности показала наличие вторичных крупномасштабных вихревых структур в расчетном домене, в от-личие от k-ε модели. Факт наличия крупномасштабных вторичных вихревых структур хорошо согласуется с экспери-ментальными данными.

Ключевые слова: эффект Ранка-Хилша, вихревая труба, моделирование турбулентности, визуализация

© Noskov A. S., Alekhin V. N., Khait A. V., Anoshin N. M., 2015

44

Russian Journal of Construction Science and Technology

A. S. Noskov, V. N. Alekhin, A. V. Khait, N. M. Anoshin

Experimental investigations, presented in the litera-ture [1–5], highlight an ultimate complexity of the flow arising in vortex tubes. For this reason there is still no general energy separation theory which takes into ac-count all physical processes arising in vortex tubes.

Numerical simulation is one of the ways to study the internal structure of the flow in vortex tube. Results of numerical simulation of Ranque-Hilsch effect are given in papers [6–10]. It was found out that turbulence models have significant influence on the results of simu-lations. For instance, Skye et al. [6] used standard k-ε tur-bulence model and received divergence of the ηS (Eq. 1) about 40 % with respect to experimental data. Farouk et al. [8] used LES turbulence model and found out a better coincidence with measured data.

Thus investigation of different turbulence models is im-portant task. The present paper is aimed to investigate and vi-sualize the air flow in Ranque-Hilsch vortex tube simulated both with standard k-ε and SAS-SST turbulence models. A detailed discussion on internal structure of the flow is given.

Numerical modelReynolds-averaged Navier–Stokes equations were

used in numerical simulations [11]:Momentum equation

r m

m

ddt

p div

Div

Vgrad V

S

= - +жиз

цшч +

+·

23

2

S

S( )

(2)

where ρ — density; V — velocity; p — static pres-sure; μΣ = μ + μt; μ — molecular viscosity; μt — turbu-

lence viscosity; S·

— strain rate tensor.Continuity equation

¶¶

+ ( ) =rr

tdiv V 0 (3)

Energy conservation equation

¶¶

( ) + ( ) -

-ж

изз

ц

шчч =

¶¶

tH div H

divc

ht

pt

p

r r

l

V

grad (4)

where H — total enthalpy; h — static enthalpy; λt/cp = = μt/Prt; λt — turbulent thermal conductivity; Prt — turbu-lent Prandtl number (Prt = 0.8 for air); cp — heat capacity.

Ideal gas state equation p RT= r (5)

where R — gas constant Standard k–ε and SAS-SST turbulence models

[12–14] were applied. Large Eddy Simulation (LES), Detached Eddy Simulation (DES) and Reynolds Stress Models (RSM) were excluded from consideration due to limitations in computational power. ANSYS CFX was used to solve equations of the model numerically.

Computational domain of the vortex tube is depicted in Fig. 2. Main dimensions of the domain are the following: energy separation chamber diameter D = 16.8 mm; dia-phragm diameter d = 9.8 mm; energy separation chamber length L = 168 mm and conical angle α = 3.5°.

The following initial conditions were used: absolute static pressure p = 105 Pa; static temperature T = 300 K; velocities Vx = Vy = Vz = 0; turbulence kinetic energy k = 0; turbulence dissipation rate ε = 0. The properties of the air were taken into consideration.

Boundary conditions:– Vortex tube inlet (flow G1, Fig. 1): absolute static

pressure p = 5·105 Pa; static temperature T = 300 К, tur-bulence intensity I = 5 %.

– Hot flow outlet (G2, Fig. 1): absolute static pres-sure p = 2.6·105 Pa. The given value of static pressure was chosen in order to obtain the cold mass flow fraction val-ue (6) φ = 0.6.

– Cold flow outlet (G3, Fig. 1): absolute static pressure p = 105 Pa.

– No slip and adiabatic wall boundary conditions were used at all solid walls.

– j =G

G3

1

(6)

where G3 — cold mass flow rate; G1 — inlet mass flow rate.

Computations were carried out in unsteady regime. Considered physical time was t = 2·10– 2 s. Time step was

Fig. 1. Schematic of vortex tube: 1 — nozzle inlet; 2 — energy separation chamber; 3 — cold flow diffuser; 4 — hot flow throttle; 5 — nozzle duct; G1 — inlet flow; G2 — hot flow outlet; G3 — cold flow outlet

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adaptive in the range of Δt = 10–5–10–7 s. Second order scheme was used for temporal integration and high reso-lution scheme was used for spatial integration.

Simulation resultsDistribution of hydrodynamic parameters in the lon-

gitudinal cross section of the vortex tube under consid-eration received with k-ε turbulence model is shown in

Fig. 3. Analysis of the plots shows that vortex core has higher static temperature as compared to outer part of the flow. In the same time total temperature has the opposite distribution. Computational streamlines are presented in Fig. 4. The air flow is of axisymmetric and reached steady state. The flow predicted with SAS-SST turbulence mod-el has significant differences with respect to the one pre-dicted with k-ε model. The flow demonstrates unsteady

Fig. 2. Vortex tube computational domain

Fig. 3. Distribution of hydrodynamic parameters received with k-ε turbulence model

Fig. 4. Streamlines in the vortex flow predicted with k-ε turbulence model

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behavior, and all hydrodynamic parameters undergo high fluctuations. Distribution of the velocity and static tem-perature in the longitudinal vortex tube cross section is presented in Fig. 5.

Streamlines plot is shown in Fig. 6 in order to vi-sualize the air flow simulated with SAS-SST turbu-

lence model. The flow is asymmetric as opposed to the one found with k-ε model. Large scale second-ary vortex structures are seen in the figure. This is the main difference between the results of k-ε and SAS-SST models.

The existence of large scale vortex structures has been detected experimentally by Arbuzov et al. [15]. Experimental visualization from [15] is shown in Fig. 7.

Vortex Core Region algorithm implemented into ANSYS CFX postprocessor has been used in order to vi-sualize secondary large-scale vortex structures predict-

ed by SAS-SST turbulence model (Fig. 8). Qualitative agreement with experimental results (Fig. 7) is achieved. Therefore we can conclude that SAS-SST turbulence model simulates internal structure of the vortex flow in a better way with respect to standard k-ε model.

Fig. 5. Distribution of hydrodynamic parameters received with SAS-SST turbulence model

Fig. 6. Streamlines in the vortex flow predicted with SAS-SST turbulence model

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Fig. 7. Experimental visualization of secondary large-scale vortex structures [15]

ConclusionVisualization of the air flow in Ranque-Hilsch vortex

tube has been performed on the basis of numerical com-putations. Standard k–ε and SAS-SST turbulence mod-els were used in the simulations. SAS-SST turbulence

model simulated unsteady vortex flow with high fluctua-tions of all hydrodynamic parameters instead k-ε model showed smooth and steady-state flow. Only SAS-SST turbulence model could predict the existence of second-ary large-scale vortex structures within the computa-tional domain. The existence of such vortex structures is confirmed by experimental results.

In conclusion, SAS-SST turbulence model is rec-ommended for further investigation of Ranque-Hilsch energy separation phenomenon because of the bet-ter correspondence to experimental studies. Accurate numerical model of energy separation effect is a pow-erful instrument for improvement of the vortex tube ge-ometry and, consequently, its efficiency.

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effekt. Eksperiment, teoriia, tekhnicheskie resheniia [Vortex ef-fect. Experiment, theory, technical solutions]. Moscow, Energomash Publ., 2000. 415 p. (In Russ.).

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Fig. 8. Visualization of large-scale vortex structures simulated numerically with SAS-SST turbulence model

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10. Khait A., Noskov A., Alekhin V. and Lovtsov A. Mathematical simulation of Ranque-Hilsch vortex tube heat and power performances. Proc. of 14th International conference on computing in civil and building engineering, 2012, Moscow, рр. 160–161.

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